Questions tagged [church-turing-thesis]

For questions about the interpretation, extension and validity of the Church-Turing thesis, the hypothesis that states that a function is effectively calculable by a human if and only if the function is computable (on a Turing machine)

I am aware of the fact that, since the concept of "effectively calculable function" is not rigorous or formally definable, the Church-Turing thesis may not be proven by symbolic or formal reasoning ...

I've read that when Turing-Church thesis is applied to the universe and physics, one of the three interpretations that we can use and is defended by some important physicists is that:
"The universe ...

The Church-Turing is a hypothesis about the nature of computable functions. It states that a function on the natural numbers is computable by a human being following an algorithm, ignoring resource ...

$S$ is a subset of the class of all recursively enumerable languages over some finite symbols then $S$ is recursively enumerable iff
If $L$ is in $S$ and $L'$ is a language such that $L ⊆ L'$ and $L'$...

I'm currently studying some of the history of computation / computability, in the early days known as recursion theory.
I see Goedel's definition of recursive functions seems significant in his paper,...

There are relativistic spacetimes (e.g. M-H spacetimes; see Hogarth 1994) where a worldline of infinite duration can be contained in the past of a finite observer. This means that a normal observer ...

So I'm currently taking discrete math II at my university and I came across a somewhat philosophical question (so I apologize if this is question is hard to answer precisely) of whether mathematicians ...

Church-Turing thesis states that any effectively computable process is computable by a TM. Let's assume for now that it means that every physical machine is computable by a TM. Let's call it A.
Now ...

I've had several Computer Science courses and, from what I recall, I've never been given a rigorous definition of suitable encoding. Definitions always tend to use effective method or some synonym to ...

When I read about the Church-Turing thesis it seems to be a common claim that "physical reality is Turing-computable." What is the basis for this claim? Are there any theoretical results along these ...

Please correct me if at any time my definitions are wrong.
Suppose we have a programming language $L$ over some set $D$ with semantic (partial) n-ary functions $\varphi^n:D \to (D^n \to D)$. Assume $L ...

According to Wikipedia, the Church-Turing thesis "states that a function on the natural numbers is computable by a human being ignoring resource limitations if and only if it is computable by a Turing ...

In my previous question ( Can Turing machines be converted into equivalent Lambda Calculus expressions with a systematic approach? ), I got the answer that it is indeed possible.
And as I have read ...

We know that Turing machines and Lambda Calculus are equivalent in power. And There are proofs for that, I'm sure.
But is there an algorithm, a systematic way for us to convert a Turing machine into ...

Church-Turing thesis : Every effectively calculable function is a TM-computable function.
But, hypercomputation models are strictly more powerful than TM and can solve TM-uncomputable problems on the ...

Computer science is a science and as a science each thesis can be refutable. So, why there is no "major" counter-thesis?
After all, Einstein was a well known "genius" and has lived a long life and he ...

From my understanding for a function to be considered Turing-computable the Turing machine which computes it must terminate for all inputs (according to this http://planetmath.org/turingcomputable and ...

As you know, an Oracle Turing Machine (OTM) is a "black box" which somehow can tell us whether a given Turing machine with a given input eventually halts. By Church's Thesis it is impossible to design ...

I know this question might seem weird, maybe I'm just overthinking, but this is really troubling me because I've been a computer engineer for some time now and conditionals (if statements for instance)...

I would like to clarify this because I see some kind of contradiction between Rice's theorem and Turing completeness.
This is the problem:
In building an Universal Turing Machine to emulate another ...

I hope my question makes sense: Starting with the premise that the untyped $\lambda $ calculus is equivalent in power to a Turing machine, to what in a Turing machine does adding types to the $\lambda ...

I have a deep appreciation for formalisms like the Turing Machine and the $\lambda$-Calculus, and enjoy studying them and learning more about how they relate to physical computers. I am now learning ...

I am doing some work on register machine theory which revolves around a 2-register register machine and attempting to show that it is not possible to compute an upper-bound on the final contents of ...

There's a lot of debate about what exactly the Church-Turing thesis is, but roughly it's the argument that "undecidable" should be considered equivalent to "undecidable by a universal turing machine."
...

If we have an algorithm that need to run $n=2$ operations and then halt, I think we could say the problem it solves, is tractable, but if $n=10^{120}$ althought It could be theoretically solvable it ...